The present invention generally relates to a field flattener used in an image forming optical system for a camera, or the like, and more particularly to a field flattener for flattening a bent image surface.
Generally in an image forming optical system, it is known from Petzval""s theorem that an image surface is bent when Petzval""s sum xcexa3 is not 0, xcexa3 being expressed as follows:   Σ  =      -                  ∑        i            ⁢              xe2x80x83            ⁢                        (                                    1              /                              n                i                                      -                          1              /                              n                                  i                  -                  1                                                              )                /                  r          i                    
where ri is a radius of curvature of an i-th surface of an optical element constituting an optical system, and ni is a refractive index. A film for a camera or a detector normally take a plane shape and are therefore incapable of being coincident with the bent image surface described above, and a different therebetween appears to be a blur of the image with the result that an image quality considerably declines. This leads to the use of an optical element called a field flattener having a function of removing a curvature of field.
FIG. 5 is an illustration of a field flattener shown in, e.g., Rundolf Kingslake, xe2x80x9cLens Design Fundamentalsxe2x80x9d (issued by Academic Press, Inc., 1978). In FIG. 5, the numeral 1 represents an image forming optical system, and a curvature of field is seen on the image surface in the case of using only this optical system. The numeral 2 denotes a field flattener and has a function of removing the curvature of field caused by the image forming optical system 1. The numeral 3 represents an image surface becoming a plane surface into which the curvature of field has been removed by the field flattener 2.
The conventional field flattener is designed based on Petzval""s sum. Namely, when Petzval""s sum held by the image forming optical system 1 is xcexa3opt, a configuration is designed so that Petzval""s sum held by the field flattener 2 becomes xe2x88x92xcexa3opt, whereby Petzval""s sum as a whole becomes 0 and the curvature on the image surface 3 is removed in a third-order aberration range. For instance, when the field flattener 2 is configured so that an object-sided surface thereof has a curvature radius rff, and an image-sided surface is formed as a plane surface, the curvature radius rff may be set as follows:       r    ff    =            1              ∑        opt              ⁢          (                        1          n                -                  1                      n            o                              )      
One-sided surface or double surfaces of the conventional field flattener 2 are constructed of spherical surfaces, wherein an image surface is flattened by changing a focal position by use of refractive power. In this case, the image-sided surface of the field flattener 2 is formed as a flat surface, while the object-sided surface is formed as a spherical surface, and the field flattener 2, when being fitted closely to the image surface, functions only as an optical element eliminating the curvature of field within the third-order aberration range. If even one of the three conditions described above is not met, however, the refractive power possessed by the field flattener 2 also exerts an influence on an image forming performance, resulting in a problem of an occurrence of a new aberration. Especially when using a detector for capturing an image, the field flattener 2 can not be closely fitted to the detector, and therefore a new aberration occurs, resulting in a decline of image quality.
The present invention, which has been devised to solve the problems described above, aims at obtaining a field flattener that causes no aberration due to the refractive power.
A field flattener having a function of flattening a bent image surface on which an image is formed through an image forming optical system according to the present invention, is characterized in that a refractive index of a material constituting the field flattener is equal to or larger than 2, a sectional configuration of the field flattener cut in an optical-axis direction containing an optical axis is formed to take a stepped shape toward a peripheral edge thereof from the optical axis, and an axial height of a stepped portion configuring a surface in the optical-axis direction in this stepped shape is equal to or larger than twice a wavelength of beams to be used. With this configuration, a distance up to an image forming point of the beams passing through the center of the field flattener and a distance up to an image forming point of the beams passing through a portion away from the center of the field flattener, are uniformized, and an aberration due to the image forming optical system is corrected, thereby obtaining a flattened image surface though its section assumes a saw-tooth shape. Further, the refractive index of the material constituting the field flattener is equal to or larger than 2, whereby a deviation from the plane surface within the image surface taking the saw-tooth shape can be reduced, and an image blur can be restrained within an allowable range.
Note that the above expression that xe2x80x9cthe sectional configuration of the field flattener cut in the optical-axis direction containing the optical axis is formed to take the stepped shape toward the peripheral edge thereof from the optical axisxe2x80x9d, includes a case where steps in the stepped shape are formed on only one of an object-sided surface and an image-sided surface of the field flattener (the other surface of the field flattener is formed with no step in the stepped shape in this case), and a case where the steps in the stepped shape are distributed to both of the object- and image-sided surfaces of the field flattener. Further, xe2x80x9cthe axial height of the stepped portion configuring the surface in the optical-axis direction in this stepped shapexe2x80x9d is an addition of axial heights of the stepped portions formed on both surfaces in the case where the steps in the stepped shape are formed in distribution to both of the object- and image-sided surfaces of the field flattener as described above.
Moreover, in the field flattener described above, an axial height d of the stepped portion configuring the surface in the optical-axis direction in the stepped shape of the field flattener is equal to or larger than twice a wavelength of beams to be used, and the field flattener is designed to meet the following formula:   d  ≤                    2        ⁢                  n          o                ⁢        n                    n        -                  n          o                      ⁢    FD  
where F is an F-value of the image forming optical system, D is a diameter of a spot size of an allowable blur, n is a refractive index of a material constituting the field flattener, and no is a refractive index of the atmospheric air. An image surface in a flat shape with a blur which is caused by the stepped portion falling within the allowable range can be thereby obtained.
Further, a difference .rm between a radius rm+1 of an (m+1)th stepped portion in the stepped shape of the field flattener and a radius rm of the m-th stepped portion therein is designed to meet the following formula:       Δ    ⁢          xe2x80x83        ⁢          r      m        ≤      2    ⁢          (                                    m            +            1                          -                  m                    )        ⁢          RFD        ⁢          (              1        -                  l          f                    )      
where F is the F-value of the image forming optical system, f is a focal length, R is a radius of curvature of a bent image surface when the field flattener is not provided, l is an interval between the image surface and the field flattener, and D is the diameter of the spot size of the allowable blur. An image surface in a much flatter configuration can be thereby obtained.
Furthermore, in the field flattener described above, an annular zone portion configuring a surface in a direction orthogonal to the optical axis in the stepped shape may be formed as a curved surface. With this configuration, aberrations such as a coma etc. are reduced, and an image forming performance can be improved.
Moreover, in the field flattener described above, the stepped portion configuring the surface in the optical-axis direction in the stepped shape may be formed in parallel to principal beam passing through the stepped portion. With this configuration, the beams traveling through the stepped portion can be minimized, and a decline of contrast due to stray light can be restrained.
Germanium, silicon or chalcogenide glass is suited as a material constituting the field flattener.
Further, in the field flattener, the thinnest portion may be formed with a through-hole. With this configuration, an aberration, which is, though small, caused by the flat plate, can be completely removed, and it is possible to avoid a decrease in transmissivity that will become a problem in the case of using a material exhibiting a large absorption.
Moreover, in the field flattener described above, the stepped shape can be processed by etching. With this configuration, the stepped shape can be processed at a high precision, and a multiplicity of field flatteners can be simultaneously processed and can be efficiently produced.